Green, with a final-round 69, held her nerve down the stretch to join China's Lin Xiyu (67) and Aditi Ashok (67) of India in the sudden-death climax before sealing her first LPGA Tour win in three-and-a-half years on the second extra hole.

The major champion showed her class in holing a 25-foot birdie putt on the last to make the play-off and then a clutch five-footer for birdie on the first extra hole to stay in the hunt with Lin after Ashok was eliminated with a par.

Playing the par-3 18th for a third time in a row, Green secured victory with a par after Lin was unable to get up and down from a greenside bunker.

The 26-year-old pocketed a cheque for US$450,000 (A$680,000) for winning her first LPGA Tour event since the Cambia Portland Classic in September 2019.

Green won the Vic Open and The Players Series Murray River in successive weeks last year in Australia but craved more success on the richest and most prestigious Tour in women's golf.

"It's been a long few years," the Perth product said, choking up with emotion.

"I played really well last year without getting a win.

"Getting across the line has been really difficult so I'm really proud of myself for hanging in there because I really didn't think that I'd be in it, with how I was playing and making so many putts.

"So I'm still really happy but other emotions are coming out right now."

It didn't look like being Green's day when she could only manage to par her first 14 holes on Sunday.

"It's been a long few years. I played really well last year without getting a win. Getting across the line has been really difficult so I'm really proud of myself for hanging in there ..." - Hannah Green.

After starting the final round two strokes behind American pacesetter Cheyenne Knight, Green couldn't buy a birdie until finally nabbing one on the par-5 15th to claim a four-way share of the lead.

But when Ashok and Lin made birdies at the last, Green had to drop a bomb to join them in the play-off at nine-under 275 for the 72 regulation holes.

"I knew you didn't need a low score today to win," she said, as the vocal Los Angeles crowd chanted "Hannah, Hannah, Hannah".

"I feel this weekend played a lot different to the first couple of days so my caddie just said 'stay patient'.

"You always try to do that but it's easier said than done.

"So I'm just really proud of holing that putt in regulation on 18 and obviously the putt on the last couple of holes."

Green is the fourth Australian in the past fortnight to win on the major tours around the world.

Grace Kim captured her maiden LPGA Tour title at the LOTTE Championship in Hawaii, before Lucas Herbert snared his third DP World Tour trophy at the ISPS Handa Championship in Japan and Mark Hensby broke through at the PGA Tour Champions Invited Celebrity Classic in Texas.

Having won the KPMG Women’s PGA Championship in 2019 before her Portland success, Green is also now the seventh Australian to have amassed at least three LPGA Tour victories, joining Katherine Kirk (3), Wendy Doolan (3), Minjee Lee (8), Rachel Hetherington (8), Jan Stephenson (16) and seven-time major champion Karrie Webb (41).

Fellow Australian Sarah Kemp closed with a 71 on Sunday to tie for 13th at seven-under, while Lee (72) finished joint 44th at one-over.